How is 0 divisible by 8?

Divisibility rule / divisible

The rules of divisibility for different numbers are covered in this article. We will explain to you what is meant by a divisibility rule and how to apply it. This article belongs to the field of math.

Is the number 231 divisible by 3 with no remainder or not? Can you divide the number 371 by 4 without a comma? The answers to this can either be determined with a pocket calculator or by using divisibility rules.

Divisibility rule 2:

A number is divisible by 2 without a remainder, if

  • the number is even (2, 4, 6, 8 etc.)
  • the last digit is even (0, 2, 4, 6, 8)

Examples:

  • The number 34 is divisible by 2 without a remainder because the last digit is even
  • The number 31 is not divisible by 2 because the last digit is odd

Divisibility rule 3:

A number is divisible by 3 without a remainder, if

  • the checksum is divisible by 3 without a remainder

Note: The checksum is the sum of all digits (e.g. the checksum of 2356 -> 2 + 3 + 5 + 6 = 16)

Examples:

  • The number 150 is divisible by 3, because 1 + 5 + 0 = 6 and 6 is divisible by 3 without a remainder
  • The number 231 is divisible by 3, because 2 + 3 + 1 = 6 and 6 is divisible by 3 without a remainder
  • The number 778 is not divisible by 3, because 7 + 7 + 8 = 22 and 22 cannot be divided by 3 without a remainder

Divisibility rule 4:

A number is divisible by 4 without a remainder, if

  • the last two digits are divisible by 4 without a remainder

Examples:

  • 340 is divisible by 4, because 40 is divisible by 4 without a remainder
  • 652 is divisible by 4, because 52 is divisible by 4 without a remainder
  • 653 is not divisible by 4, because 53 is not divisible by 4 without a remainder

Divisibility rule 5:

A number is divisible by 5 without a remainder, if

  • the last digit of the number is a 0 or 5

Examples:

  • 250 is divisible by 5 without a remainder, because the last digit of the number is a 0
  • 275 is divisible by 5 without a remainder, because the last digit of the number is 5
  • 272 is not divisible by 5 without a remainder, because the last digit is a 2

Divisibility rule 6:

A number is divisible by 6 without a remainder, if

  • the number is divisible by 2 and by 3 without a remainder

Examples:

  • 12 is divisible by 6 with no remainder, because 12 is divisible by 2 and 3 with no remainder
  • 28 is not divisible by 6 without a remainder, because 28 by 3 results in a number with a remainder / decimal point

Divisibility rule 8:

A number is divisible by 8 without a remainder, if

  • the last three digits are divisible by 8 without a remainder

Examples:

  • 2016 is divisible by 8 without a remainder, because 16: 8 = 2
  • 2808 is divisible by 8 without a remainder, because 808: 8 = 101
  • 9218 is not divisible by 8, because 218: 8 results in a decimal point

Divisibility rule 9:

A number is divisible by 9 without a remainder, if

  • the checksum is divisible by 9 without a remainder

Note: The checksum is the sum of all digits (e.g. the checksum of 2356 -> 2 + 3 + 5 + 6 = 16)

Examples:

  • The number 153 is divisible by 9 without a remainder, because 1 + 5 + 3 = 9 and 9: 9 = 1
  • The number 515 is not divisible by 9 without a remainder, because 5 + 1 + 5 = 11 and not divisible by 9 without a remainder

Divisibility rule 10:

The number is divisible by 10 with no remainder, if

  • the last digit of the number is a 0

Examples:

  • 2010 is divisible by 10 without a remainder, because the last digit is 0
  • 2011 is not divisible by 10 without a remainder, because the last digit is not a 0

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